The chemical family composed of elements that have full valence shells is the noble gases.

Here's why:

* Valence Shell: This is the outermost electron shell of an atom.

* Full Valence Shell: A full valence shell means the outermost shell is completely filled with electrons, making the atom very stable and unreactive.

* Noble Gases: This group of elements (Helium, Neon, Argon, Krypton, Xenon, Radon) are located in Group 18 of the periodic table. Their electron configurations naturally result in a full valence shell, making them extremely inert and unlikely to form chemical bonds.

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